CN114239306A - Double-sided cooling fuel serious accident process simulation method - Google Patents

Double-sided cooling fuel serious accident process simulation method Download PDF

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CN114239306A
CN114239306A CN202111587780.0A CN202111587780A CN114239306A CN 114239306 A CN114239306 A CN 114239306A CN 202111587780 A CN202111587780 A CN 202111587780A CN 114239306 A CN114239306 A CN 114239306A
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CN114239306B (en
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张亚培
吴世浩
王栋
苏光辉
田文喜
秋穗正
季松涛
何晓军
史晓磊
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Xian Jiaotong University
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Abstract

The invention discloses a double-sided cooling fuel serious accident process simulation method, which comprises the following steps: 1. setting calculation parameters of the double-sided cooling fuel; 2. carrying out initialization calculation; 3. judging the type of the node; 4. calculating the node temperature rise process; 5. calculating the oxidation melting process; 6. calculating a melt migration process; 7. repeating steps 3 to 6 until a specified calculation time is reached. The method can quickly and accurately calculate the behaviors of heating, oxidation, melting, melt repositioning and the like of the double-sided cooling fuel under the working condition of serious accidents, and has important significance for analyzing the process of the serious accidents of the double-sided cooling fuel.

Description

Double-sided cooling fuel serious accident process simulation method
Technical Field
The invention belongs to the field of calculation of a double-sided cooling fuel severe accident process under a nuclear reactor severe accident, and particularly relates to a double-sided cooling fuel severe accident process simulation method.
Background
In a severe accident of a nuclear reactor, a series of processes such as oxidation, rupture, melting and melt relocation of materials in the reactor occur. The rapid and accurate simulation of the severe accident process of the nuclear reactor core has important significance for the prediction of accident development and the designation of accident mitigation measures.
Colleges and research institutions at home and abroad carry out a lot of research on the traditional rod-shaped fuel and develop corresponding rod-shaped fuel serious accident simulation software. The double-sided cooling fuel is used as one of novel fuels, and is rarely researched by colleges and universities and research institutions at home and abroad, and due to the structural particularity of the double-sided cooling fuel, the traditional rod-shaped fuel serious accident simulation software cannot carry out analysis and calculation on the serious accident progress of the double-sided cooling fuel.
Disclosure of Invention
In order to fill the research blank of the prior art, the invention provides a double-sided cooling fuel serious accident progress simulation method which can quickly and accurately simulate and calculate the processes of heating, oxidation, melting, inner and outer side melt relocation and the like of double-sided cooling fuel in a nuclear power plant serious accident.
In order to achieve the purpose, the invention adopts the technical scheme that:
a double-sided cooling fuel serious accident process simulation method comprises the following steps:
step 1: setting calculation parameters of the double-sided cooling fuel:
Figure BDA0003428171960000011
the geometric dimensions and mass of the fuel pellets, inner cladding, outer cladding;
Figure BDA0003428171960000012
the number of the fuel, the number of the radial nodes and the number of the axial nodes, wherein each radial node at least comprises a double-sided cooling fuel;
Figure BDA0003428171960000021
overall power variation and power factor of each node;
Figure BDA0003428171960000022
the coolant pressure and coolant level change with time;
Figure BDA0003428171960000023
coolant temperature and flow at the fuel bottom inlet over time;
Figure BDA0003428171960000024
the ambient boundary temperature of the fuel as a function of time;
Figure BDA0003428171960000025
an initial temperature of each node;
Figure BDA0003428171960000026
calculating a time step and a specified calculation time;
step 2: developing an initialization calculation
Performing initial calculation on the temperatures of the fuel pellets, the inner cladding and the outer cladding in each node of the double-sided cooling fuel by using boundary conditions at the initial calculation time; due to the particularity of the double-sided cooling fuel, the position of the heat insulation surface of the fuel pellet is assumed during calculation, then the position of the heat insulation surface is updated through iterative solution, the real position of the heat insulation surface is finally determined, and the temperature of the fuel pellet in each node, the temperature of the inner package shell and the temperature of the outer package shell are obtained;
and step 3: node type determination
In the process of a serious accident, the appearance of the double-sided cooling fuel is changed greatly, so that in order to carry out the analysis of the serious accident rapidly, the double-sided cooling fuel in each node is treated equivalently as one, and the geometric forms of the inner and outer nodes of the double-sided cooling fuel in the process of the serious accident are fixedly divided respectively;
the outside node geometrical morphology of the double-sided cooling fuel is divided into the following five types:
type 1: the outer sides of the double-sided cooling fuel are not contacted with each other, the columnar shape is still maintained, and the porosity of the outer sides is greater than that of the outer sides
Figure BDA0003428171960000027
Type 2: the inner and outer envelopes both shatter and the double-sided cooling fuel collapses;
type 3: the outside of the double-sided cooling fuel is contacted with each other, the column shape is not maintained any more, and the porosity of the outside is more than 0 and less than
Figure BDA0003428171960000028
Type 4: the space between the outer sides of the double-sided cooling fuel is completely blocked, and the porosity of the outer sides is equal to 0;
type 5: the outer sides of the double-sided cooling fuel are completely blocked, and the melting share is more than 99 percent.
The inside node geometries of the double-sided cooling fuel are divided into the following four types:
type 1: the inner side of the double-sided cooling fuel is not blocked and still maintains a cylindrical shape, and the porosity of the inner side is more than 0;
type 2: the inner and outer envelopes both shatter and the double-sided cooling fuel collapses;
type 4: the inner side of the double-sided cooling fuel is completely blocked, and the porosity of the inner side is equal to 0;
type 5: the inner side of the double-sided cooling fuel is completely blocked, and the melting share is more than 99%.
The node type 3 does not exist on the inner side of the double-sided cooling fuel, and due to the particularity of the double-sided cooling fuel, the double-sided cooling fuel collapses only after the cladding on the inner side and the cladding on the outer side are cracked, and the node is the type 2;
and 4, step 4: node temperature rise process calculation
Calculating the heat exchange inside the nodes and the heat exchange between the nodes in the node heating process;
1) heat exchange within a node
Based on the division of the node types at two sides of the double-sided cooling fuel, the calculation is carried out respectively considering the two conditions that the node types at the inner side and the outer side are both type 1 and one side of the node types at the inner side and the outer side is not type 1 when the heat exchange calculation is carried out inside the node;
the types of the inner and outer side nodes are type 1
When the types of the inner and outer side nodes of the double-sided cooling fuel are both type 1, the heat transfer among the fuel pellets, the outer shell, the inner shell, the outer coolant and the inner coolant of the nodes is considered in detail; assuming that the coolant temperatures inside and outside the fuel in the same node are consistent, the energy conservation differential equation for each component is established as follows:
Figure BDA0003428171960000031
Figure BDA0003428171960000041
Figure BDA0003428171960000042
Figure BDA0003428171960000043
Figure BDA0003428171960000044
in the formula:
Figure BDA0003428171960000045
represents the fuel pellet temperature;
Figure BDA0003428171960000046
represents the outer envelope temperature;
Figure BDA0003428171960000047
represents the inner envelope temperature;
Figure BDA0003428171960000048
represents the outside coolant temperature;
Figure BDA0003428171960000049
represents the inside coolant temperature;
Figure BDA00034281719600000410
represents the specific heat capacity of the fuel pellets;
Figure BDA00034281719600000411
represents the specific heat capacity of the outer envelope;
Figure BDA00034281719600000412
represents the specific heat capacity of the inner packaging shell;
Figure BDA00034281719600000413
represents the outside coolant specific heat capacity;
Figure BDA00034281719600000414
represents the inside coolant specific heat capacity;
Figure BDA00034281719600000415
represents the fuel pellet mass;
Figure BDA00034281719600000416
representing the outer envelope quality;
Figure BDA00034281719600000417
indicating the inclusion of chitinAn amount;
Figure BDA00034281719600000418
represents the outboard coolant mass;
Figure BDA00034281719600000419
represents the inboard coolant mass; t represents time; d represents a differential sign;
Figure BDA00034281719600000420
representing the heat transfer coefficient between the fuel pellet and the outer cladding;
Figure BDA00034281719600000421
representing the heat transfer coefficient between the fuel pellet and the inner package shell;
Figure BDA00034281719600000422
representing the heat transfer coefficient between the fuel pellets and the outside coolant;
Figure BDA00034281719600000423
representing the heat transfer coefficient between the fuel pellets and the inside coolant;
Figure BDA00034281719600000424
representing the heat transfer coefficient between the outer envelope and the outside coolant;
Figure BDA00034281719600000425
representing the heat transfer coefficient between the inner jacket and the inside coolant;
Figure BDA00034281719600000426
representing the heat transfer coefficient between the fuel pellet and the outer cladding;
Figure BDA00034281719600000427
representing the heat transfer coefficient between the fuel pellet and the inner package shell;
Figure BDA00034281719600000428
representing the heat transfer coefficient between the fuel pellets and the outside coolant;
Figure BDA00034281719600000429
representing the heat transfer coefficient between the fuel pellets and the inside coolant;
Figure BDA00034281719600000430
representing the heat transfer coefficient between the outer envelope and the outside coolant;
Figure BDA00034281719600000431
representing the heat transfer coefficient between the inner jacket and the inside coolant;
Figure BDA00034281719600000432
a heat source representing fuel pellets;
Figure BDA00034281719600000433
a heat source representing an outer envelope;
Figure BDA00034281719600000434
a heat source representing the inner envelope;
and solving the temperature change condition and the energy change condition in each component in the node based on the differential equation.
②, one side of the node types at the inner side and the outer side is not type 1
When one of the node types of the inner side and the outer side of the double-sided cooling fuel is not type 1, the fuel pellet, the outer shell and the inner shell are regarded as a whole by adopting a lumped parameter method, and the average temperature T of one node is usednTo calculate the total heat exchange amount between the double-sided cooling fuel and the outside coolant
Figure BDA0003428171960000051
And the total amount of heat exchange between the dual-sided cooling fuel and the inside coolant
Figure BDA0003428171960000052
The energy conservation differential equation at this time is as follows:
Figure BDA0003428171960000053
Figure BDA0003428171960000054
Figure BDA0003428171960000055
in the formula:
Figure BDA0003428171960000056
representing the product of the mass of the fuel pellets in the node and the specific heat capacity of the fuel pellets plus the product of the mass of the outer cladding and the specific heat capacity of the outer cladding plus the product of the mass of the inner cladding and the specific heat capacity of the inner cladding; t isnRepresents the node average temperature;
when heat exchange inside the node is solved, for the liquid coolant with weak fluidity, the temperature of the coolant on the inner side is assumed to be consistent with that of the coolant on the outer side; for gaseous coolant, assuming that the flow of the gaseous coolant is a quasi-steady state process, firstly assuming an insulating surface of a double-sided cooling fuel during solving, calculating the heat exchange amount of the fuel to the coolant on two sides by taking the insulating surface as a reference, further calculating the temperature of fuel pellets on two sides of the insulating surface, correcting the insulating surface when the temperature difference of the fuel pellets on two sides of the insulating surface is greater than 0.5K, determining the final position of the insulating surface through repeated iteration, and solving the temperature change condition and the energy change condition in each component in a node;
2) heat transfer between nodes
The heat exchange between the nodes comprises axial heat exchange and radial heat exchange, and the heat exchange is processed by adopting a lumped parameter method; after the total heat exchange quantity between the nodes is calculated, the average temperature change of the nodes is obtained, and the temperature change condition and the energy change condition in each component in each node are further calculated;
axial heat exchange between the nodes calculates the total axial heat exchange quantity between the nodes according to a Fourier law:
Figure BDA0003428171960000061
in the formula: q represents the axial total heat exchange quantity between the nodes; lambda represents the average heat transfer coefficient between nodes; a represents the effective heat exchange area between nodes; Δ T represents the average temperature difference between nodes; Δ x represents the center distance between nodes;
because the inner side surfaces of the double-sided cooling fuel are mutually independent, the radiation heat exchange between the inner side surfaces of the nodes is not considered;
when the porosity of the outer side of the node is not 0 and the coolant is gas, the radial radiation heat exchange quantity between the nodes is approximately calculated by adopting the following equation:
Figure BDA0003428171960000062
in the formula: qrad,iRepresenting the radial radiation heat exchange quantity between the nodes; σ represents Stefan-Boltzmann constant; a. theiRepresenting the effective radiation area between nodes; t isi、Ti+1Respectively representing the node average temperature of the node i and the node i + 1; n is a radical ofr,i Nr,i+1Respectively representing the number of double-sided cooling fuels of a node i and a node i +1, and enabling N to be arranged at the outermost noder,i+1＝2；
Due to the relocation of the melt, when the porosity of the nodes is 0, the radial heat exchange between the nodes is calculated by adopting the same method as the axial heat exchange between the nodes;
if the porosity of the node is 0 and the melting quality of the node is greater than 0, the influence of the upward, lateral and downward heat transfer quantity of the molten pool on the heat exchange between the nodes is also considered when calculating the heat exchange quantity between the nodes, and the corresponding heat exchange coefficient is expressed as follows:
Figure BDA0003428171960000063
Figure BDA0003428171960000064
Figure BDA0003428171960000065
in the formula:
Figure BDA0003428171960000071
respectively representing the upward heat exchange coefficient, the downward heat exchange coefficient and the lateral wall of the molten pool; k is a radical ofcRepresents the thermal conductivity; r represents the characteristic height of the molten pool; ra represents the Rayleigh number of the molten pool;
in addition, with the continuous melting of the double-sided cooling fuel and the repositioning of the melt, empty nodes may appear at the upper part in the later period of an accident, and at the moment, heat exchange calculation is not carried out on the empty nodes; when the heat exchange calculation is carried out on the nodes below the empty nodes, only the radiation heat exchange of the nodes on the upper boundary is considered;
and 5: calculation of Oxidation melting progress
Along with the temperature rise of the inner and outer cladding of the double-sided cooling fuel, the inner and outer cladding can react with water to generate zirconium water, release a large amount of chemical heat and generate hydrogen; the amount of increase in oxygen mass in the cladding oxide was calculated using the following parabolic equation:
Figure BDA0003428171960000072
in the formula, WmRepresents the mass increase of the oxide; t represents time; km(T) represents an oxidation rate constant;
comparing the energy of each component in the node with the energy when the components are completely melted, and judging whether each component is melted; due to the interaction between the materials, the cladding will dissolve the fuel pellets and the cladding oxides, the dissolution distance being calculated using the following hoffman kinetic energy relationship:
Figure BDA0003428171960000073
Figure BDA0003428171960000074
in the formula (I), the compound is shown in the specification,
Figure BDA0003428171960000075
represents the fuel pellet dissolution distance; daIndicating a cladding oxide dissolution distance;
Figure BDA0003428171960000076
represents the fuel pellet dissolution rate constant; kaRepresenting the cladding oxide dissolution rate constant; t represents time;
step 6: melt migration Process calculation
1) Node energy calculation
When the accumulated damage share of the inner side or the outer side cladding of the double-sided cooling fuel reaches 100% and the thickness of the oxide of the cladding is smaller than the minimum thickness which is customized by a user and prevents the cladding from cracking, the cladding can crack, and liquid melt in the node can start to migrate downwards along the crack; calculating a node each time from the top node center line to the outside and from top to bottom in the downward migration process of the melt;
the energy equation for each node is represented by:
Figure BDA0003428171960000081
in the formula: u represents the total energy of the node; u represents the specific heat of the node; m represents the node quality; t represents time; d represents a differential sign;
in order to integrate the node energy equation, integrating the variables m and u respectively by adopting a separation variable method, and assuming that the variables m and u do not influence each other; the calculation steps are as follows:
firstly, assuming that the node quality does not change with time in a time step, the energy change rate in the heat transfer process is as follows:
Figure BDA0003428171960000082
secondly, the total energy of the nodes is updated as follows according to the initial energy:
Figure BDA0003428171960000083
and thirdly, assuming that the updated specific heat in the process of melt migration does not change along with time in a time step, the energy change rate is as follows:
Figure BDA0003428171960000084
fourthly, using the same time step length to obtain the total energy after updating as follows:
Figure BDA0003428171960000085
in the formula, Δ t represents a time step; m is0Representing the node quality at the initial time; u shape0Representing the node energy at the initial time; u. of1Representing the specific heat of the node at the end of the time step; u shape1Representing the total energy of the node obtained by integrating only specific heat u; u shape2Representing the total energy of the resulting node.
2) Calculation of the amount of inboard and outboard melt migration
Separately calculating the migration processes of the melts at the inner side and the outer side of the double-sided cooling fuel, wherein the migration amount of the inner melt between nodes and the migration amount of the outer melt between nodes are calculated by adopting the following models; the node where the melt flows out in the model is called a source node, and the node where the melt is received is called a receiving node; the model calculation steps are as follows:
comprehensively considering two flow mechanisms of film flow and pipe flow, calculating the mass flow of the melt flowing out of a source node:
mass flow rate of the film-like flow: wf＝rcdfufXfN(22)
Tubular flow mass flow:
Figure BDA0003428171960000091
and finally determining the mass flow: MIN (W ═ MINp,Wf,mρc/Δt)(24)
In the formula, WfRepresenting the film-like flow mass flow; r iscDenotes the melt density; dfRepresents the steady state liquid film thickness; u. offRepresents the average flow rate; xfRepresents the wet week of melt flow; g represents the gravitational acceleration; h issA drive ram is indicated; f represents a friction coefficient; l isrIndicating the length of the receiving node; dhRepresents the hydraulic diameter; wpRepresenting tubular flow mass flow; a. therRepresenting the area within the source node; m isrcRepresenting the melt mass at the source node; Δ t represents a time step; MIN means taking the minimum value in the following brackets; w represents the final determined mass flow;
secondly, calculating the mass of the condensed melt in the receiving node, wherein the calculation formula is as follows:
mfz＝ρcXfNLδc/2 (25)
in the formula, mfzRepresents the mass of melt condensed in the receiving node; l issRepresenting the source node length;
thirdly, calculating the quality of the molten mass to be transferred in the receiving node, wherein the calculation formula is as follows:
mac＝ΔtW-MAX(ΔtrW,mfz) (26)
in the formula, macRepresenting the amount of melt to be migrated in the receiving node; Δ trRepresents the time required for the melt to flow to the bottom of the receiving node; MAX denotes taking the maximum value in the following brackets;
3) mass exchange calculation in molten pool
If the porosity of the node is 0 and the melting mass of the node is greater than 0, considering mass exchange between the nodes due to natural circulation in the melting tank and assuming that all components in the melting tank reach the same concentration within a characteristic time constant, the calculation formula is as follows:
f(t)＝fo+(ff-fo)(1-e-τ/t) (27)
wherein f (t) represents the change in the concentration of the node component with time; f. ofoRepresenting the initial concentration of the node component; f. offRepresenting the final concentration of the components after the quality exchange of the adjacent nodes; τ represents a characteristic time constant; t represents time;
and 7: and repeating the steps 3 to 6 until the specified calculation time is reached.
Compared with the prior art, the invention has the following advantages:
1. the invention can consider the structural characteristics of the double-sided cooling fuel and carry out the simulation calculation of the serious accident process of the double-sided cooling fuel.
2. The invention can simulate the processes of heating, oxidizing, melting and melt repositioning of the double-sided cooling fuel.
3. Aiming at the state of double-sided cooling fuel in an inside and outside serious accident, the invention divides five types of node types for the outside of the fuel and four types of node types for the inside of the fuel.
4. The invention adopts different calculation methods aiming at different node types of the double-sided cooling fuel in the severe process, and has high calculation speed and less calculation resource requirements.
5. The invention has no limit on the number of rods of the double-sided cooling fuel subjected to analog calculation, can carry out verification calculation on the out-of-reactor rod bundle experiment, and can also carry out analysis calculation on the reactor core of the reactor.
Drawings
FIG. 1 is a flow chart of a double-sided cooling fuel severe accident process simulation method.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
As shown in FIG. 1, the double-sided cooling fuel serious accident process simulation method of the invention comprises the following steps:
step 1: setting the calculation parameters of the double-sided cooling fuel as follows: the geometric dimensions and mass of the fuel pellets, inner cladding, outer cladding; the number of the fuel, the number of the radial nodes and the number of the axial nodes, wherein each radial node at least comprises a double-sided cooling fuel; overall power variation and power factor of each node; the coolant pressure and coolant level change with time; coolant temperature and flow at the fuel bottom inlet over time; the ambient boundary temperature of the fuel as a function of time; an initial temperature of each node; calculating a time step and a specified calculation time;
step 2: developing an initialization calculation
Performing initial calculation on the temperatures of the fuel pellets, the inner cladding and the outer cladding in each node of the double-sided cooling fuel by using boundary conditions at the initial calculation time; due to the particularity of the double-sided cooling fuel, the position of the heat insulation surface of the fuel pellet is assumed during calculation, the fuel pellet is divided into two parts by taking the heat insulation surface as a reference, the heat transfer quantity of the fuel pellet towards the inner side and the outer side is calculated respectively, the temperature of the fuel pellet at the two sides of the heat insulation surface is further determined, if the temperature difference value of the fuel pellet at the two sides of the heat insulation surface is larger than 0.5K, the position of the heat insulation surface is updated, the node temperature solving calculation is carried out again until the real position of the heat insulation surface is finally determined, and the temperature of the fuel pellet in each node, the inner wrapping shell and the outer wrapping shell is obtained;
and step 3: node type determination
In the process of a serious accident, the appearance of the double-sided cooling fuel is changed greatly, so that in order to carry out the analysis of the serious accident rapidly, the double-sided cooling fuel in each node is treated equivalently as one, and the geometric forms of the inner and outer nodes of the double-sided cooling fuel in the process of the serious accident are fixedly divided respectively;
the outside node geometrical morphology of the double-sided cooling fuel is divided into the following five types:
type 1: the outer sides of the double-sided cooling fuel are not contacted with each other, the columnar shape is still maintained, and the porosity of the outer sides is greater than that of the outer sides
Figure BDA0003428171960000111
Type 2: the inner and outer envelopes both shatter and the double-sided cooling fuel collapses;
type 3: the outside of the double-sided cooling fuel is contacted with each other, the column shape is not maintained any more, and the porosity of the outside is more than 0 and less than
Figure BDA0003428171960000121
Type 4: the space between the outer sides of the double-sided cooling fuel is completely blocked, and the porosity of the outer sides is equal to 0;
type 5: the outer sides of the double-sided cooling fuel are completely blocked, and the melting share is more than 99 percent.
The inside node geometries of the double-sided cooling fuel are divided into the following four types:
type 1: the inner side of the double-sided cooling fuel is not blocked and still maintains a cylindrical shape, and the porosity of the inner side is more than 0;
type 2: the inner and outer envelopes both shatter and the double-sided cooling fuel collapses;
type 4: the inner side of the double-sided cooling fuel is completely blocked, and the porosity of the inner side is equal to 0;
type 5: the inner side of the double-sided cooling fuel is completely blocked, and the melting share is more than 99%.
The node type 3 does not exist on the inner side of the double-sided cooling fuel, and due to the particularity of the double-sided cooling fuel, the double-sided cooling fuel collapses only after the cladding on the inner side and the cladding on the outer side are cracked, and the node is the type 2;
and 4, step 4: node temperature rise process calculation
Calculating the heat exchange inside the nodes and the heat exchange between the nodes in the node heating process;
1) heat exchange within a node
Based on the division of the node types at two sides of the double-sided cooling fuel, the calculation is carried out respectively considering the two conditions that the node types at the inner side and the outer side are both type 1 and one side of the node types at the inner side and the outer side is not type 1 when the heat exchange calculation is carried out inside the node;
the types of the inner and outer side nodes are type 1
When the types of the inner and outer side nodes of the double-sided cooling fuel are both type 1, the heat transfer among the fuel pellets, the outer shell, the inner shell, the outer coolant and the inner coolant of the nodes is considered in detail; assuming that the coolant temperatures inside and outside the fuel in the same node are consistent, the energy conservation differential equation for each component is established as follows:
Figure BDA0003428171960000131
Figure BDA0003428171960000132
Figure BDA0003428171960000133
Figure BDA0003428171960000134
Figure BDA0003428171960000135
in the formula:
Figure BDA0003428171960000136
represents the fuel pellet temperature;
Figure BDA0003428171960000137
represents the outer envelope temperature;
Figure BDA0003428171960000138
represents the inner envelope temperature;
Figure BDA0003428171960000139
represents the outside coolant temperature;
Figure BDA00034281719600001310
represents the inside coolant temperature;
Figure BDA00034281719600001311
represents the specific heat capacity of the fuel pellets;
Figure BDA00034281719600001312
represents the specific heat capacity of the outer envelope;
Figure BDA00034281719600001313
represents the specific heat capacity of the inner packaging shell;
Figure BDA00034281719600001314
represents the outside coolant specific heat capacity;
Figure BDA00034281719600001315
represents the inside coolant specific heat capacity;
Figure BDA00034281719600001316
represents the fuel pellet mass;
Figure BDA00034281719600001317
representing the outer envelope quality;
Figure BDA00034281719600001318
representing the inner cladding quality;
Figure BDA00034281719600001319
represents the outboard coolant mass;
Figure BDA00034281719600001320
represents the inboard coolant mass; t represents time; d represents a differential sign;
Figure BDA00034281719600001321
representing the heat transfer coefficient between the fuel pellet and the outer cladding;
Figure BDA00034281719600001322
representing the heat transfer coefficient between the fuel pellet and the inner package shell;
Figure BDA00034281719600001323
representing the heat transfer coefficient between the fuel pellets and the outside coolant;
Figure BDA00034281719600001324
representing the heat transfer coefficient between the fuel pellets and the inside coolant;
Figure BDA00034281719600001325
representing the heat transfer coefficient between the outer envelope and the outside coolant;
Figure BDA00034281719600001326
representing the heat transfer coefficient between the inner jacket and the inside coolant;
Figure BDA00034281719600001327
representing the heat transfer coefficient between the fuel pellet and the outer cladding;
Figure BDA00034281719600001328
representing the heat transfer coefficient between the fuel pellet and the inner package shell;
Figure BDA00034281719600001329
representing the heat transfer coefficient between the fuel pellets and the outside coolant;
Figure BDA00034281719600001330
representing the heat transfer coefficient between the fuel pellets and the inside coolant;
Figure BDA00034281719600001331
representing the heat transfer coefficient between the outer envelope and the outside coolant;
Figure BDA00034281719600001332
representing the heat transfer coefficient between the inner jacket and the inside coolant;
Figure BDA00034281719600001333
a heat source representing fuel pellets;
Figure BDA00034281719600001334
a heat source representing an outer envelope;
Figure BDA00034281719600001335
a heat source representing the inner envelope;
and solving the temperature change condition and the energy change condition in each component in the node based on the differential equation.
②, one side of the node types at the inner side and the outer side is not type 1
When one of the node types of the inner side and the outer side of the double-sided cooling fuel is not type 1, the fuel pellet, the outer shell and the inner shell are regarded as a whole by adopting a lumped parameter method, and the average temperature T of one node is usednTo calculate the total heat exchange amount between the double-sided cooling fuel and the outside coolant
Figure BDA0003428171960000141
And the total amount of heat exchange between the dual-sided cooling fuel and the inside coolant
Figure BDA0003428171960000142
The energy conservation differential equation at this time is as follows:
Figure BDA0003428171960000143
Figure BDA0003428171960000144
Figure BDA0003428171960000145
in the formula:
Figure BDA0003428171960000146
representing the product of the mass of the fuel pellets in the node and the specific heat capacity of the fuel pellets plus the product of the mass of the outer cladding and the specific heat capacity of the outer cladding plus the product of the mass of the inner cladding and the specific heat capacity of the inner cladding; t isnRepresents the node average temperature;
when heat exchange inside the node is solved, for the liquid coolant with weak fluidity, the temperature of the coolant on the inner side is assumed to be consistent with that of the coolant on the outer side; for gaseous coolant, assuming that the flow of the gaseous coolant is a quasi-steady state process, firstly assuming an insulating surface of a double-sided cooling fuel during solving, calculating the heat exchange amount of the fuel to the coolant on two sides by taking the insulating surface as a reference, further calculating the temperature of fuel pellets on two sides of the insulating surface, correcting the insulating surface when the temperature difference of the fuel pellets on two sides of the insulating surface is greater than 0.5K, determining the final position of the insulating surface through repeated iteration, and solving the temperature change condition and the energy change condition in each component in a node;
2) heat transfer between nodes
The heat exchange between the nodes comprises axial heat exchange and radial heat exchange, and the heat exchange is processed by adopting a lumped parameter method; after the total heat exchange quantity between the nodes is calculated, the average temperature change of the nodes is obtained, and the temperature change condition and the energy change condition in each component in each node are further calculated;
axial heat exchange between the nodes calculates the total axial heat exchange quantity between the nodes according to a Fourier law:
Figure BDA0003428171960000151
in the formula: q represents the axial total heat exchange quantity between the nodes; lambda represents the average heat transfer coefficient between nodes; a represents the effective heat exchange area between nodes; Δ T represents the average temperature difference between nodes; Δ x represents the center distance between nodes;
because the inner side surfaces of the double-sided cooling fuel are mutually independent, the radiation heat exchange between the inner side surfaces of the nodes is not considered;
when the porosity of the outer side of the node is not 0 and the coolant is gas, the radial radiation heat exchange quantity between the nodes is approximately calculated by adopting the following equation:
Figure BDA0003428171960000152
in the formula: qrad,iRepresenting the radial radiation heat exchange quantity between the nodes; σ represents Stefan-Boltzmann constant; a. theiRepresenting the effective radiation area between nodes; t isi、Ti+1Respectively representing the node average temperature of the node i and the node i + 1; n is a radical ofr,i Nr,i+1Respectively representing the number of double-sided cooling fuels of a node i and a node i +1, and enabling N to be arranged at the outermost noder,i+1＝2；
Due to the relocation of the melt, when the porosity of the nodes is 0, the radial heat exchange between the nodes is calculated by adopting the same method as the axial heat exchange between the nodes;
if the porosity of the node is 0 and the melting quality of the node is greater than 0, the influence of the upward, lateral and downward heat transfer quantity of the molten pool on the heat exchange between the nodes is also considered when calculating the heat exchange quantity between the nodes, and the corresponding heat exchange coefficient is expressed as follows:
Figure BDA0003428171960000153
Figure BDA0003428171960000161
Figure BDA0003428171960000162
in the formula:
Figure BDA0003428171960000163
respectively representing the upward heat exchange coefficient, the downward heat exchange coefficient and the lateral wall of the molten pool; k is a radical ofcRepresents the thermal conductivity; r represents the characteristic height of the molten pool; ra represents the Rayleigh number of the molten pool;
in addition, with the continuous melting of the double-sided cooling fuel and the repositioning of the melt, empty nodes may appear at the upper part in the later period of an accident, and at the moment, heat exchange calculation is not carried out on the empty nodes; when the heat exchange calculation is carried out on the nodes below the empty nodes, only the radiation heat exchange of the nodes on the upper boundary is considered;
and 5: calculation of Oxidation melting progress
Along with the temperature rise of the inner and outer cladding of the double-sided cooling fuel, the inner and outer cladding can react with water to generate zirconium water, release a large amount of chemical heat and generate hydrogen; the amount of increase in oxygen mass in the cladding oxide was calculated using the following parabolic equation:
Figure BDA0003428171960000164
in the formula, WmRepresents the mass increase of the oxide; t represents time; km(T) represents an oxidation rate constant;
comparing the energy of each component in the node with the energy when the components are completely melted, and judging whether each component is melted; due to the interaction between the materials, the cladding will dissolve the fuel pellets and the cladding oxides, the dissolution distance being calculated using the following hoffman kinetic energy relationship:
Figure BDA0003428171960000165
Figure BDA0003428171960000166
in the formula (I), the compound is shown in the specification,
Figure BDA0003428171960000167
represents the fuel pellet dissolution distance; daIndicating a cladding oxide dissolution distance;
Figure BDA0003428171960000168
represents the fuel pellet dissolution rate constant; kaRepresenting the cladding oxide dissolution rate constant; t represents time;
step 6: melt migration Process calculation
1) Node energy calculation
When the accumulated damage share of the inner side or the outer side cladding of the double-sided cooling fuel reaches 100% and the thickness of the oxide of the cladding is smaller than the minimum thickness which is customized by a user and prevents the cladding from cracking, the cladding can crack, and liquid melt in the node can start to migrate downwards along the crack; calculating a node each time from the top node center line to the outside and from top to bottom in the downward migration process of the melt;
the energy equation for each node is represented by:
Figure BDA0003428171960000171
in the formula: u represents the total energy of the node; u represents the specific heat of the node; m represents the node quality; t represents time; d represents a differential sign;
in order to integrate the node energy equation, integrating the variables m and u respectively by adopting a separation variable method, and assuming that the variables m and u do not influence each other; the calculation steps are as follows:
firstly, assuming that the node quality does not change with time in a time step, the energy change rate in the heat transfer process is as follows:
Figure BDA0003428171960000172
secondly, the total energy of the nodes is updated as follows according to the initial energy:
Figure BDA0003428171960000173
and thirdly, assuming that the updated specific heat in the process of melt migration does not change along with time in a time step, the energy change rate is as follows:
Figure BDA0003428171960000174
fourthly, using the same time step length to obtain the total energy after updating as follows:
Figure BDA0003428171960000181
in the formula, Δ t represents a time step; m is0Representing the node quality at the initial time; u shape0Representing the node energy at the initial time; u. of1Representing the specific heat of the node at the end of the time step; u shape1Representing the total energy of the node obtained by integrating only specific heat u; u shape2Representing the total energy of the resulting node.
2) Calculation of the amount of inboard and outboard melt migration
Separately calculating the migration processes of the melts at the inner side and the outer side of the double-sided cooling fuel, wherein the migration amount of the inner melt between nodes and the migration amount of the outer melt between nodes are calculated by adopting the following models; the node where the melt flows out in the model is called a source node, and the node where the melt is received is called a receiving node; the model calculation steps are as follows:
comprehensively considering two flow mechanisms of film flow and pipe flow, calculating the mass flow of the melt flowing out of a source node:
mass flow rate of the film-like flow: wf＝rcdfufXfN (22)
Tubular flow mass flow:
Figure BDA0003428171960000182
and finally determining the mass flow: MIN (W ═ MINp,Wf,mρc/Δt) (24)
In the formula, WfRepresenting the film-like flow mass flow; r iscDenotes the melt density; dfRepresents the steady state liquid film thickness; u. offRepresents the average flow rate; xfRepresents the wet week of melt flow; g represents the gravitational acceleration; h issA drive ram is indicated; f represents a friction coefficient; l isrIndicating the length of the receiving node; dhRepresents the hydraulic diameter; wpRepresenting tubular flow mass flow; a. therRepresenting the area within the source node;mrcrepresenting the melt mass at the source node; Δ t represents a time step; MIN means taking the minimum value in the following brackets; w represents the final determined mass flow;
secondly, calculating the mass of the condensed melt in the receiving node, wherein the calculation formula is as follows:
mfz＝ρcXfNLδc/2 (25)
in the formula, mfzRepresents the mass of melt condensed in the receiving node; l issRepresenting the source node length;
thirdly, calculating the quality of the molten mass to be transferred in the receiving node, wherein the calculation formula is as follows:
mac＝ΔtW-MAX(ΔtrW,mfz) (26)
in the formula, macRepresenting the amount of melt to be migrated in the receiving node; Δ trRepresents the time required for the melt to flow to the bottom of the receiving node; MAX denotes taking the maximum value in the following brackets;
3) mass exchange calculation in molten pool
If the porosity of the node is 0 and the melting mass of the node is greater than 0, considering mass exchange between the nodes due to natural circulation in the melting tank and assuming that all components in the melting tank reach the same concentration within a characteristic time constant, the calculation formula is as follows:
f(t)＝fo+(ff-fo)(1-e-τ/t) (27)
wherein f (t) represents the change in the concentration of the node component with time; f. ofoRepresenting the initial concentration of the node component; f. offRepresenting the final concentration of the components after the quality exchange of the adjacent nodes; τ represents a characteristic time constant; t represents time;
and 7: and repeating the steps 3 to 6 until the specified calculation time is reached.
While the invention has been described in further detail with reference to specific preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A double-sided cooling fuel serious accident process simulation method is characterized by comprising the following steps: the method comprises the following steps:
step 1: setting calculation parameters of the double-sided cooling fuel:
Figure FDA0003428171950000011
the geometric dimensions and mass of the fuel pellets, inner cladding, outer cladding;
Figure FDA0003428171950000012
the number of the fuel, the number of the radial nodes and the number of the axial nodes, wherein each radial node at least comprises a double-sided cooling fuel;
Figure FDA0003428171950000013
overall power variation and power factor of each node;
Figure FDA0003428171950000014
the coolant pressure and coolant level change with time;
Figure FDA0003428171950000015
coolant temperature and flow at the fuel bottom inlet over time;
Figure FDA0003428171950000016
the ambient boundary temperature of the fuel as a function of time;
Figure FDA0003428171950000017
an initial temperature of each node;
Figure FDA0003428171950000018
calculating a time step and a specified calculation time;
step 2: developing an initialization calculation
Performing initial calculation on the temperatures of the fuel pellets, the inner cladding and the outer cladding in each node of the double-sided cooling fuel by using boundary conditions at the initial calculation time; due to the particularity of the double-sided cooling fuel, the position of the heat insulation surface of the fuel pellet is assumed during calculation, then the position of the heat insulation surface is updated through iterative solution, the real position of the heat insulation surface is finally determined, and the temperature of the fuel pellet in each node, the temperature of the inner package shell and the temperature of the outer package shell are obtained;
and step 3: node type determination
In the process of a serious accident, the appearance of the double-sided cooling fuel is changed greatly, so that in order to carry out the analysis of the serious accident rapidly, the double-sided cooling fuel in each node is treated equivalently as one, and the geometric forms of the inner and outer nodes of the double-sided cooling fuel in the process of the serious accident are fixedly divided respectively;
the outside node geometrical morphology of the double-sided cooling fuel is divided into the following five types:
type 1: the outer sides of the double-sided cooling fuel are not contacted with each other, the columnar shape is still maintained, and the porosity of the outer sides is greater than that of the outer sides
Figure FDA0003428171950000021
Type 2: the inner and outer envelopes both shatter and the double-sided cooling fuel collapses;
type 3: the outside of the double-sided cooling fuel is contacted with each other, the column shape is not maintained any more, and the porosity of the outside is more than 0 and less than
Figure FDA0003428171950000022
Type 4: the space between the outer sides of the double-sided cooling fuel is completely blocked, and the porosity of the outer sides is equal to 0;
type 5: the outer sides of the double-sided cooling fuel are completely blocked, and the melting share is more than 99 percent.
The inside node geometries of the double-sided cooling fuel are divided into the following four types:
type 1: the inner side of the double-sided cooling fuel is not blocked and still maintains a cylindrical shape, and the porosity of the inner side is more than 0;
type 2: the inner and outer envelopes both shatter and the double-sided cooling fuel collapses;
type 4: the inner side of the double-sided cooling fuel is completely blocked, and the porosity of the inner side is equal to 0;
type 5: the inner side of the double-sided cooling fuel is completely blocked, and the melting share is more than 99%.
The node type 3 does not exist on the inner side of the double-sided cooling fuel, and due to the particularity of the double-sided cooling fuel, the double-sided cooling fuel collapses only after the cladding on the inner side and the cladding on the outer side are cracked, and the node is the type 2;
and 4, step 4: node temperature rise process calculation
Calculating the heat exchange inside the nodes and the heat exchange between the nodes in the node heating process;
1) heat exchange within a node
Based on the division of the node types at two sides of the double-sided cooling fuel, the calculation is carried out respectively considering the two conditions that the node types at the inner side and the outer side are both type 1 and one side of the node types at the inner side and the outer side is not type 1 when the heat exchange calculation is carried out inside the node;
the types of the inner and outer side nodes are type 1
When the types of the inner and outer side nodes of the double-sided cooling fuel are both type 1, the heat transfer among the fuel pellets, the outer shell, the inner shell, the outer coolant and the inner coolant of the nodes is considered in detail; assuming that the coolant temperatures inside and outside the fuel in the same node are consistent, the energy conservation differential equation for each component is established as follows:
Figure FDA0003428171950000031
Figure FDA0003428171950000032
Figure FDA0003428171950000033
Figure FDA0003428171950000034
Figure FDA0003428171950000035
in the formula:
Figure FDA0003428171950000036
represents the fuel pellet temperature;
Figure FDA0003428171950000037
represents the outer envelope temperature;
Figure FDA0003428171950000038
represents the inner envelope temperature;
Figure FDA0003428171950000039
represents the outside coolant temperature;
Figure FDA00034281719500000310
represents the inside coolant temperature;
Figure FDA00034281719500000311
represents the specific heat capacity of the fuel pellets;
Figure FDA00034281719500000312
represents the specific heat capacity of the outer envelope;
Figure FDA00034281719500000313
represents the specific heat capacity of the inner packaging shell;
Figure FDA00034281719500000314
represents the outside coolant specific heat capacity;
Figure FDA00034281719500000315
represents the inside coolant specific heat capacity;
Figure FDA00034281719500000316
represents the fuel pellet mass;
Figure FDA00034281719500000317
representing the outer envelope quality;
Figure FDA00034281719500000318
representing the inner cladding quality;
Figure FDA00034281719500000319
represents the outboard coolant mass;
Figure FDA00034281719500000320
represents the inboard coolant mass; t represents time; d represents a differential sign;
Figure FDA00034281719500000321
representing the heat transfer coefficient between the fuel pellet and the outer cladding;
Figure FDA00034281719500000322
representing the heat transfer coefficient between the fuel pellet and the inner package shell;
Figure FDA00034281719500000323
representing the heat transfer coefficient between the fuel pellets and the outside coolant;
Figure FDA00034281719500000324
representing the heat transfer coefficient between the fuel pellets and the inside coolant;
Figure FDA00034281719500000325
representing the heat transfer coefficient between the outer envelope and the outside coolant;
Figure FDA00034281719500000326
representing the heat transfer coefficient between the inner jacket and the inside coolant;
Figure FDA00034281719500000327
representing the heat transfer coefficient between the fuel pellet and the outer cladding;
Figure FDA00034281719500000328
representing the heat transfer coefficient between the fuel pellet and the inner package shell;
Figure FDA00034281719500000329
representing the heat transfer coefficient between the fuel pellets and the outside coolant;
Figure FDA0003428171950000041
representing the heat transfer coefficient between the fuel pellets and the inside coolant;
Figure FDA0003428171950000042
representing the heat transfer coefficient between the outer envelope and the outside coolant;
Figure FDA0003428171950000043
representing the heat transfer coefficient between the inner jacket and the inside coolant;
Figure FDA0003428171950000044
to representA heat source for the fuel pellets;
Figure FDA0003428171950000045
a heat source representing an outer envelope;
Figure FDA0003428171950000046
a heat source representing the inner envelope;
and solving the temperature change condition and the energy change condition in each component in the node based on the differential equation.
②, one side of the node types at the inner side and the outer side is not type 1
When one of the node types of the inner side and the outer side of the double-sided cooling fuel is not type 1, the fuel pellet, the outer shell and the inner shell are regarded as a whole by adopting a lumped parameter method, and the average temperature T of one node is usednTo calculate the total heat exchange amount between the double-sided cooling fuel and the outside coolant
Figure FDA0003428171950000047
And the total amount of heat exchange between the dual-sided cooling fuel and the inside coolant
Figure FDA0003428171950000048
The energy conservation differential equation at this time is as follows:
Figure FDA0003428171950000049
Figure FDA00034281719500000410
Figure FDA00034281719500000411
in the formula:
Figure FDA00034281719500000412
representing the product of the mass of the fuel pellets in the node and the specific heat capacity of the fuel pellets plus the product of the mass of the outer cladding and the specific heat capacity of the outer cladding plus the product of the mass of the inner cladding and the specific heat capacity of the inner cladding; t isnRepresents the node average temperature;
when heat exchange inside the node is solved, for the liquid coolant with weak fluidity, the temperature of the coolant on the inner side is assumed to be consistent with that of the coolant on the outer side; for gaseous coolant, assuming that the flow of the gaseous coolant is a quasi-steady state process, firstly assuming an insulating surface of a double-sided cooling fuel during solving, calculating the heat exchange amount of the fuel to the coolant on two sides by taking the insulating surface as a reference, further calculating the temperature of fuel pellets on two sides of the insulating surface, correcting the insulating surface when the temperature difference of the fuel pellets on two sides of the insulating surface is greater than 0.5K, determining the final position of the insulating surface through repeated iteration, and solving the temperature change condition and the energy change condition in each component in a node;
2) heat transfer between nodes
The heat exchange between the nodes comprises axial heat exchange and radial heat exchange, and the heat exchange is processed by adopting a lumped parameter method; after the total heat exchange quantity between the nodes is calculated, the average temperature change of the nodes is obtained, and the temperature change condition and the energy change condition in each component in each node are further calculated;
axial heat exchange between the nodes calculates the total axial heat exchange quantity between the nodes according to a Fourier law:
Figure FDA0003428171950000051
in the formula: q represents the axial total heat exchange quantity between the nodes; lambda represents the average heat transfer coefficient between nodes; a represents the effective heat exchange area between nodes; Δ T represents the average temperature difference between nodes; Δ x represents the center distance between nodes;
because the inner side surfaces of the double-sided cooling fuel are mutually independent, the radiation heat exchange between the inner side surfaces of the nodes is not considered;
when the porosity of the outer side of the node is not 0 and the coolant is gas, the radial radiation heat exchange quantity between the nodes is approximately calculated by adopting the following equation:
Figure FDA0003428171950000052
in the formula: qrad,iRepresenting the radial radiation heat exchange quantity between the nodes; σ represents Stefan-Boltzmann constant; a. theiRepresenting the effective radiation area between nodes; t isi、Ti+1Respectively representing the node average temperature of the node i and the node i + 1; n is a radical ofr,i Nr,i+1Respectively representing the number of double-sided cooling fuels of a node i and a node i +1, and enabling N to be arranged at the outermost noder,i+1＝2；
Due to the relocation of the melt, when the porosity of the nodes is 0, the radial heat exchange between the nodes is calculated by adopting the same method as the axial heat exchange between the nodes;
if the porosity of the node is 0 and the melting quality of the node is greater than 0, the influence of the upward, lateral and downward heat transfer quantity of the molten pool on the heat exchange between the nodes is also considered when calculating the heat exchange quantity between the nodes, and the corresponding heat exchange coefficient is expressed as follows:
Figure FDA0003428171950000061
Figure FDA0003428171950000062
Figure FDA0003428171950000063
in the formula:
Figure FDA0003428171950000064
respectively representing the upward heat exchange coefficient, the downward heat exchange coefficient and the lateral wall of the molten pool; k is a radical ofcRepresents the thermal conductivity; r represents the characteristic height of the molten pool; ra denotes the bathThe Rayleigh number;
in addition, with the continuous melting of the double-sided cooling fuel and the repositioning of the melt, empty nodes may appear at the upper part in the later period of an accident, and at the moment, heat exchange calculation is not carried out on the empty nodes; when the heat exchange calculation is carried out on the nodes below the empty nodes, only the radiation heat exchange of the nodes on the upper boundary is considered;
and 5: calculation of Oxidation melting progress
Along with the temperature rise of the inner and outer cladding of the double-sided cooling fuel, the inner and outer cladding can react with water to generate zirconium water, release a large amount of chemical heat and generate hydrogen; the amount of increase in oxygen mass in the cladding oxide was calculated using the following parabolic equation:
Figure FDA0003428171950000065
in the formula, WmRepresents the mass increase of the oxide; t represents time; km(T) represents an oxidation rate constant;
comparing the energy of each component in the node with the energy when the components are completely melted, and judging whether each component is melted; due to the interaction between the materials, the cladding will dissolve the fuel pellets and the cladding oxides, the dissolution distance being calculated using the following hoffman kinetic energy relationship:
Figure FDA0003428171950000066
Figure FDA0003428171950000067
in the formula (I), the compound is shown in the specification,
Figure FDA0003428171950000068
represents the fuel pellet dissolution distance; daIndicating a cladding oxide dissolution distance;
Figure FDA0003428171950000069
represents the fuel pellet dissolution rate constant; kaRepresenting the cladding oxide dissolution rate constant; t represents time;
step 6: melt migration Process calculation
1) Node energy calculation
When the accumulated damage share of the inner side or the outer side cladding of the double-sided cooling fuel reaches 100% and the thickness of the oxide of the cladding is smaller than the minimum thickness which is customized by a user and prevents the cladding from cracking, the cladding can crack, and liquid melt in the node can start to migrate downwards along the crack; calculating a node each time from the top node center line to the outside and from top to bottom in the downward migration process of the melt;
the energy equation for each node is represented by:
Figure FDA0003428171950000071
in the formula: u represents the total energy of the node; u represents the specific heat of the node; m represents the node quality; t represents time; d represents a differential sign;
in order to integrate the node energy equation, integrating the variables m and u respectively by adopting a separation variable method, and assuming that the variables m and u do not influence each other; the calculation steps are as follows:
firstly, assuming that the node quality does not change with time in a time step, the energy change rate in the heat transfer process is as follows:
Figure FDA0003428171950000072
secondly, the total energy of the nodes is updated as follows according to the initial energy:
Figure FDA0003428171950000073
and thirdly, assuming that the updated specific heat in the process of melt migration does not change along with time in a time step, the energy change rate is as follows:
Figure FDA0003428171950000081
fourthly, using the same time step length to obtain the total energy after updating as follows:
Figure FDA0003428171950000082
in the formula, Δ t represents a time step; m is0Representing the node quality at the initial time; u shape0Representing the node energy at the initial time; u. of1Representing the specific heat of the node at the end of the time step; u shape1Representing the total energy of the node obtained by integrating only specific heat u; u shape2Representing the total energy of the resulting node.
2) Calculation of the amount of inboard and outboard melt migration
Separately calculating the migration processes of the melts at the inner side and the outer side of the double-sided cooling fuel, wherein the migration amount of the inner melt between nodes and the migration amount of the outer melt between nodes are calculated by adopting the following models; the node where the melt flows out in the model is called a source node, and the node where the melt is received is called a receiving node; the model calculation steps are as follows:
comprehensively considering two flow mechanisms of film flow and pipe flow, calculating the mass flow of the melt flowing out of a source node:
mass flow rate of the film-like flow: wf＝rcdfufXfN (22)
Tubular flow mass flow:
Figure FDA0003428171950000083
and finally determining the mass flow: MIN (W ═ MINp,Wf,mρc/Δt) (24)
In the formula, WfRepresenting the film-like flow mass flow; r iscDenotes the melt density; dfRepresents the steady state liquid film thickness; u. offRepresents the average flow rate; xfRepresents the wet week of melt flow; g represents the gravitational acceleration; h issA drive ram is indicated; f represents a friction coefficient; l isrIndicating the length of the receiving node; dhRepresents the hydraulic diameter; wpRepresenting tubular flow mass flow; a. therRepresenting the area within the source node; m isrcRepresenting the melt mass at the source node; Δ t represents a time step; MIN means taking the minimum value in the following brackets; w represents the final determined mass flow;
secondly, calculating the mass of the condensed melt in the receiving node, wherein the calculation formula is as follows:
mfz＝ρcXfNLδc/2 (25)
in the formula, mfzRepresents the mass of melt condensed in the receiving node; l issRepresenting the source node length;
thirdly, calculating the quality of the molten mass to be transferred in the receiving node, wherein the calculation formula is as follows:
mac＝ΔtW-MAX(ΔtrW,mfz) (26)
in the formula, macRepresenting the amount of melt to be migrated in the receiving node; Δ trRepresents the time required for the melt to flow to the bottom of the receiving node; MAX denotes taking the maximum value in the following brackets;
3) mass exchange calculation in molten pool
If the porosity of the node is 0 and the melting mass of the node is greater than 0, considering mass exchange between the nodes due to natural circulation in the melting tank and assuming that all components in the melting tank reach the same concentration within a characteristic time constant, the calculation formula is as follows:
f(t)＝fo+(ff-fo)(1-e-τ/t) (27)
wherein f (t) represents the change in the concentration of the node component with time; f. ofoRepresenting the initial concentration of the node component; f. offRepresenting the final concentration of the components after the quality exchange of the adjacent nodes; τ denotesA characteristic time constant; t represents time;
and 7: and repeating the steps 3 to 6 until the specified calculation time is reached.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140185243A1 (en) * 2012-12-27 2014-07-03 Hyundai Motor Company Heat sink-integrated double-sided cooled power module
CN107451398A (en) * 2017-07-07 2017-12-08 西安交通大学 PWR nuclear power plant major accident analysis method
CN112289468A (en) * 2020-09-27 2021-01-29 西安交通大学 Experimental device and method for determining ultra-high temperature oxidation melting behavior of double-sided cooling fuel
CN113435004A (en) * 2021-05-25 2021-09-24 上海交通大学 Method and device for calculating migration quality of molten material in reactor core melting process

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140185243A1 (en) * 2012-12-27 2014-07-03 Hyundai Motor Company Heat sink-integrated double-sided cooled power module
CN107451398A (en) * 2017-07-07 2017-12-08 西安交通大学 PWR nuclear power plant major accident analysis method
CN112289468A (en) * 2020-09-27 2021-01-29 西安交通大学 Experimental device and method for determining ultra-high temperature oxidation melting behavior of double-sided cooling fuel
CN113435004A (en) * 2021-05-25 2021-09-24 上海交通大学 Method and device for calculating migration quality of molten material in reactor core melting process

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
许芝春 等: "堆芯熔融物与混凝土相互作用数值模拟研究", 《核动力工程》 *

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